For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with a° = 33, the value of x° is 147.

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

5a + 2a = 7a

An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

b - 1 < \( \frac{b}{-6} \)
-6 x (b - 1) < b
(-6 x b) + (-6 x -1) < b
-6b + 6 < b
-6b + 6 - b < 0
-6b - b < -6
-7b < -6
b < \( \frac{-6}{-7} \)
b < \(\frac{6}{7}\)